In a general sense, adaptive filters are systems that vary through time because the characteristics of its inputs may be varying. That is what separates it from classical digital signal processing - the digital system itself changes through time. In a sense, its convolution properties are evolving.
Therefore, adaptive filters must be non-linear because superposition does not hold. But when their adjustments are held constant after adaptation, then some can become linear, and belong under the well-named class linear adaptive filters. We will be working with those in this project.
Whenever there is a requirement to process signals in an environment of unknown statistics, adaptive filters will more often than not do the job better than a fixed filter.
The best way to introduce adaptive filters is by example. Say you are talking on you cell phone in your car, and the engine is producing unwanted noise that the cell phone must filter out. Well, when you change gears, the noise will be at a different frequency, and you don't want to stop in the middle of your conversation and toy with the electronics in your phone to adjust the band pass. The filter must do the job for you, without your intervention. An adaptive filter can track that noise, follow its characteristics, and knock it out so that you may have a good, clean conversation.
Other applications besides noise cancellation include system identification, signal prediction, source separation, channel equalization, and more.
This project is an introduction to adaptive filters. A summation of what we learned and put together:
- General theory
- What's the math involved
- What's the algorithm
- What's it for
- Simulation in MATLAB with Least Mean Squared algorithm
- Noise cancellation
- FIR identification
- Implementation of noise cancellation in real-time with TI DSP board